The average shape of a fluctuation: universality in excursions of stochastic processes

Andrea Baldassarri, Francesca Colaiori and Claudio Castellano

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Abstract: We study the average shape of a fluctuation of a time series x(t), that is the average value _T before x(t) first returns, at time T, to its initial value x(0). For large classes of stochastic processes we find that a scaling law of the form _T = T^\alpha f(t/T) is obeyed. The scaling function f(s) is to a large extent independent of the details of the single increment distribution, while it encodes relevant statistical information on the presence and nature of temporal correlations in the process. We discuss the relevance of these results for Barkhausen noise in magnetic systems.

Date: 2003-01
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Published in Phys. Rev. Lett. 90, 060601 (2003)

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